This notebook contains the key visualizations for the Task Mapping paper.

Very useful decision boundary plotting code from: https://mhahsler.github.io/Introduction_to_Data_Mining_R_Examples/book/classification-alternative-techniques.html#k-nearest-neighbors


decisionplot <- function(model, data, class_var, 
  predict_type = c("class", "prob"), resolution = 5 * 75) {
  # resolution is set to 75 dpi if the image is rendered  5 inces wide. 
  
  y <- data %>% pull(class_var)
  x <- data %>% dplyr::select(-all_of(class_var))
  
  # resubstitution accuracy
  prediction <- predict(model, x, type = predict_type[1])
  # LDA returns a list
  if(is.list(prediction)) prediction <- prediction$class
  prediction <- factor(prediction, levels = levels(y))
  
  cm <- confusionMatrix(data = prediction, reference = y)
  acc <- cm$overall["Accuracy"]
  
  # evaluate model on a grid
  r <- sapply(x[, 1:2], range, na.rm = TRUE)
  xs <- seq(r[1,1], r[2,1], length.out = resolution)
  ys <- seq(r[1,2], r[2,2], length.out = resolution)
  g <- cbind(rep(xs, each = resolution), rep(ys, time = resolution))
  colnames(g) <- colnames(r)
  g <- as_tibble(g)
  
  ### guess how to get class labels from predict
  ### (unfortunately not very consistent between models)
  cl <- predict(model, g, type = predict_type[1])
  
  # LDA returns a list
  if(is.list(cl)) { 
    prob <- cl$posterior
    cl <- cl$class
  } else
    try(prob <- predict(model, g, type = predict_type[2]))
  
  # we visualize the difference in probability/score between the 
  # winning class and the second best class.
  # don't use probability if predict for the classifier does not support it.
  max_prob <- 1
  try({
    max_prob <- t(apply(prob, MARGIN = 1, sort, decreasing = TRUE))
    max_prob <- max_prob[,1] - max_prob[,2]
  }, silent = TRUE) 
  
  cl <- factor(cl, levels = levels(y))
  
  g <- g %>% add_column(prediction = cl, probability = max_prob)
  
  ggplot(g, mapping = aes_string(
    x = colnames(g)[1],
    y = colnames(g)[2])) +
    geom_raster(mapping = aes(fill = prediction, alpha = probability)) +
     geom_contour(mapping = aes(z = as.numeric(prediction)), 
      bins = length(levels(cl)), size = .5, color = "black") +
    geom_point(data = data, mapping =  aes_string(
      x = colnames(data)[1],
      y = colnames(data)[2],
      shape = class_var), alpha = .7) + 
    scale_alpha_continuous(range = c(0,1), limits = c(0,1), guide = "none") +  
    labs(subtitle = paste("Training accuracy:", round(acc, 2)))
}

Load the Data

task_map <- read_csv('../task_map.csv')
Rows: 102 Columns: 25-- Column specification ----------------------------------------------------------------------------------------
Delimiter: ","
chr  (1): task
dbl (24): Q1concept_behav, Q3type_1_planning, Q4type_2_generate, Q6type_5_cc, Q7type_7_battle, Q8type_8_perf...
i Use `spec()` to retrieve the full column specification for this data.
i Specify the column types or set `show_col_types = FALSE` to quiet this message.

Fitting and Visualizing Models for the Task Map.

x <- combined_data %>% select(PC1, PC2, synergy, task)
train <- tasks_with_dv %>% select(PC1, PC2, synergy, task)
model <- train %>% svm(synergy ~ PC1 + PC2, data = ., kernel = "linear")

svmplot <- decisionplot(model, x, class_var = "synergy") + 
  geom_point(data = train, aes(x = PC1, y = PC2, shape = synergy), color = "darkolivegreen2", show.legend = F) +
  geom_label(data = train, aes(label = task ), nudge_y = 0.1, size = 3) +
  labs(title = "SVM (Linear Kernel)") +
  theme_minimal(base_size = 12)

svmplot
  
ggsave('svmplot_synthetic_data.png', width = 12, height = 5)

model <- train %>% knn3(synergy ~ PC1 + PC2, data = ., k = 1)

knnplot <- decisionplot(model, x, class_var = "synergy") +
  geom_point(data = train, aes(x = PC1, y = PC2, shape = synergy), color = "darkolivegreen2", show.legend = F) +
  geom_label(data = train, aes(label = task ), nudge_y = 0.1, size = 3) +
  labs(title = "kNN (1 neighbor)") + 
  theme_minimal(base_size = 12)

knnplot
  
ggsave('knnplot_synthetic_data.png', width = 12, height = 5)

---
title: "R Notebook for Paper-Related Visualizations"
output: html_notebook
---

This notebook contains the key visualizations for the Task Mapping paper.

```{r}
library(factoextra)
library(NbClust)
library(cluster)
library(plotly)
library(ggplot2)
library(caret) #for knn
library(e1071) #for svm
library(dplyr)
library(tidyverse)
```

Very useful decision boundary plotting code from: https://mhahsler.github.io/Introduction_to_Data_Mining_R_Examples/book/classification-alternative-techniques.html#k-nearest-neighbors
```{r decisionplot}

decisionplot <- function(model, data, class_var, 
  predict_type = c("class", "prob"), resolution = 5 * 75) {
  # resolution is set to 75 dpi if the image is rendered  5 inces wide. 
  
  y <- data %>% pull(class_var)
  x <- data %>% dplyr::select(-all_of(class_var))
  
  # resubstitution accuracy
  prediction <- predict(model, x, type = predict_type[1])
  # LDA returns a list
  if(is.list(prediction)) prediction <- prediction$class
  prediction <- factor(prediction, levels = levels(y))
  
  cm <- confusionMatrix(data = prediction, reference = y)
  acc <- cm$overall["Accuracy"]
  
  # evaluate model on a grid
  r <- sapply(x[, 1:2], range, na.rm = TRUE)
  xs <- seq(r[1,1], r[2,1], length.out = resolution)
  ys <- seq(r[1,2], r[2,2], length.out = resolution)
  g <- cbind(rep(xs, each = resolution), rep(ys, time = resolution))
  colnames(g) <- colnames(r)
  g <- as_tibble(g)
  
  ### guess how to get class labels from predict
  ### (unfortunately not very consistent between models)
  cl <- predict(model, g, type = predict_type[1])
  
  # LDA returns a list
  if(is.list(cl)) { 
    prob <- cl$posterior
    cl <- cl$class
  } else
    try(prob <- predict(model, g, type = predict_type[2]))
  
  # we visualize the difference in probability/score between the 
  # winning class and the second best class.
  # don't use probability if predict for the classifier does not support it.
  max_prob <- 1
  try({
    max_prob <- t(apply(prob, MARGIN = 1, sort, decreasing = TRUE))
    max_prob <- max_prob[,1] - max_prob[,2]
  }, silent = TRUE) 
  
  cl <- factor(cl, levels = levels(y))
  
  g <- g %>% add_column(prediction = cl, probability = max_prob)
  
  ggplot(g, mapping = aes_string(
    x = colnames(g)[1],
    y = colnames(g)[2])) +
    geom_raster(mapping = aes(fill = prediction, alpha = probability)) +
     geom_contour(mapping = aes(z = as.numeric(prediction)), 
      bins = length(levels(cl)), size = .5, color = "black") +
    geom_point(data = data, mapping =  aes_string(
      x = colnames(data)[1],
      y = colnames(data)[2],
      shape = class_var), alpha = .7) + 
    scale_alpha_continuous(range = c(0,1), limits = c(0,1), guide = "none") +  
    labs(subtitle = paste("Training accuracy:", round(acc, 2)))
}
```

# Load the Data
```{r}
task_map <- read_csv('../task_map.csv')
```

# Plot the Task Map and other Related Images

Draw the task map using PCA & clustering

First, run the PCA
```{r, fig.width=16, fig.height=5}
set.seed(1)

pca <- task_map %>% #select(-continuous_questions) %>%
  select(-task) %>%
  prcomp(center = T)

# get optimal number of clusters -- "silhouette" method
fviz_nbclust(x = pca$x, FUNcluster = stats::kmeans, method = "silhouette") +
  labs(subtitle = "Silhouette method")

# get optimal number of clusters
NbClust(data = pca$x, distance = "euclidean",
        min.nc = 2, max.nc = 15, method = "kmeans")

kmeans_output <- pca$x %>% 
  kmeans(centers = 3, nstart = 100)

combined_data <- cbind(task_map,
      pca$x, factor(kmeans_output$cluster)) %>%
  rename(cluster = `factor(kmeans_output$cluster)`)

fviz_eig(pca)
```

Standard Task Map Image with All Labels
```{r, fig.width=14, fig.height=5}
p <- combined_data %>%
  ggplot(aes(
    x = PC1,
    y = PC2,
    label = task,
    fill = cluster
  )) + geom_point() + geom_label(nudge_y = 0.1, size = 4) +
  
  #+ , alpha=0.05) +
# highlights only the ones in the selected set
  # geom_label(
  #   data = subset(combined_data, task %in% c("NASA Moon survival", "Desert survival")),
  #   aes(
  #     x = PC1,
  #     y = PC2,
  #     label = task ,
  #     fill = cluster
  #   ),
  #   nudge_y = 0.1,
  #   size = 2
  # )
 theme_light(base_size = 24)

p # show the plot

ggsave(plot = p, filename = '../task-map.png')
```

Task Map Image Highlighting Specific Subsets (for Illustrative Purposes)
```{r, fig.width=14, fig.height=5}
# An illustrative set to display
display_set <- c('Writing story',
 'Advertisement writing', 
 'Desert survival',
 'NASA Moon survival',
 'Ultimatum game (various versions)',
 'Dictator game and its variants',
 'Prisoner\'s Dilemma (various versions)',
 '9 Dot Problem',
 'Word construction from a subset of letters',
 'Typing game',
 'Ravens Matrices',
 'Euclidean traveling salesperson'
 )

# A set of the tasks that are most different
max_diff_set <- c('Shopping plan',
 'Minimal Group Paradigm (study diversity)',
 '9 Dot Problem',
 'Whac-A-Mole',
 'Bullard Houses',
 'Putting food into categories',
 'Checkers',
 'Reproducing arts',
 'Allocating resources to programs',
 'Image rating',
 'Arithmetic problem 2')

# A set of tasks that are the most similar
min_diff_set <- c('Arithmetic problem 1',
 'Euclidean traveling salesperson',
 'Abstract grid task',
 'Mastermind',
 'Logic Problem',
 'Guessing the correlation',
 'Random dot motion',
 'Letters-to-numbers problems (cryptography)',
 'Computer maze',
 'Recall images',
 'Recall stories')

# A set of tasks that illustrates opportunities to add new tasks
display_limitations_set <- c('Recall word lists',
                             'Hidden figures in a picture (Recall Task)',
                             'Recall images',
                             'Recall stories',
                             'Recall videos',
                             'Writing story',
                             'Advertisement writing')


graph_illustrative_plots <- function(displayset, filename){
  p <- combined_data %>%
  ggplot(aes(
    x = PC1,
    y = PC2,
    #label = task,
    #fill = cluster
    )) + geom_point(aes(size = 4)) +
  #geom_point(aes(color = cluster, size = 4)) +
#highlights only the ones in the selected set
geom_point(data = subset(combined_data, task %in% displayset), aes(size = 4),
           color = "firebrick1") +
geom_label(
  data = subset(combined_data, task %in% displayset),
  aes(
    x = PC1,
    y = PC2,
    label = task
  ),
  nudge_y = 0.15,
  size = 4
) +
 theme_minimal(base_size = 18) + theme(legend.position = "none")  

p

ggsave(plot = p, filename = filename, width = 14, height = 5)
}
```

```{r, fig.width=14, fig.height=5}
graph_illustrative_plots(display_limitations_set, '../images/task-map_with_new_task_opportunities_highlighted.png')

graph_illustrative_plots(max_diff_set, '../images/task-map_with_max_diff_highlighted.png')

# graph_illustrative_plots(min_diff_set, '../images/task-map_with_min_diff_highlighted.png')
```

Create a cool 3D version
```{r}
plot_ly(
  x = combined_data$PC1,
  y = combined_data$PC2,
  z = combined_data$PC3,
  type = "scatter3d",
  mode = "markers", # can use mode = "text"
  text = combined_data$task ,
  color = combined_data$cluster
)
```

Create synthetic dependent variable based on the clusters
```{r}
tasks_with_dv <- subset(combined_data, task %in% max_diff_set) %>%
  mutate(
    synergy = as.factor(ifelse(cluster == 1 | cluster == 2, 1, 0))
  )
combined_data <- combined_data %>%
  mutate(
    synergy = as.factor(ifelse(cluster == 1 | cluster == 2, 1, 0))
  )
```

# Fitting and Visualizing Models for the Task Map.

```{r}
x <- combined_data %>% select(PC1, PC2, synergy, task)
train <- tasks_with_dv %>% select(PC1, PC2, synergy, task)
model <- train %>% svm(synergy ~ PC1 + PC2, data = ., kernel = "linear")

svmplot <- decisionplot(model, x, class_var = "synergy") + 
  geom_point(data = train, aes(x = PC1, y = PC2, shape = synergy), color = "darkolivegreen2", show.legend = F) +
  geom_label(data = train, aes(label = task ), nudge_y = 0.1, size = 3) +
  labs(title = "SVM (Linear Kernel)") +
  theme_minimal(base_size = 12)

svmplot
  
ggsave('svmplot_synthetic_data.png', width = 12, height = 5)
```

```{r}
model <- train %>% knn3(synergy ~ PC1 + PC2, data = ., k = 1)

knnplot <- decisionplot(model, x, class_var = "synergy") +
  geom_point(data = train, aes(x = PC1, y = PC2, shape = synergy), color = "darkolivegreen2", show.legend = F) +
  geom_label(data = train, aes(label = task ), nudge_y = 0.1, size = 3) +
  labs(title = "kNN (1 neighbor)") + 
  theme_minimal(base_size = 12)

knnplot
  
ggsave('knnplot_synthetic_data.png', width = 12, height = 5)
```